Answer
$\sqrt{35}+\sqrt{5}-\sqrt{42}-\sqrt{6}$
Work Step by Step
Using $(a+b)(c+d)=ab+ad+bc+bd$ or the FOIL Method, the expression $
\left( \sqrt{5}-\sqrt{6} \right)\left( \sqrt{7}+1 \right)
$ simplifies to
\begin{array}{l}
\sqrt{5}\left( \sqrt{7} \right)+\sqrt{5}\left( 1 \right)-\sqrt{6}\left( \sqrt{7} \right)-\sqrt{6}\left( 1 \right)
\\\\=
\sqrt{35}+\sqrt{5}-\sqrt{42}-\sqrt{6}
.\end{array}
